Simulation of Sound Waves Using the Lattice Boltzmann Method for Fluid Flow: Benchmark Cases for Outdoor Sound Propagation.

Erik M. Salomons,Walter J. A. Lohman,Han Zhou,Andrew Baggaley

doi:10.1371/journal.pone.0147206

Erik M. Salomons, Walter J. A. Lohman + Show 2 more

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https://doi.org/10.1371/journal.pone.0147206

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Abstract

Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-field propagation, propagation over porous and non-porous ground, propagation over a noise barrier, and propagation in an atmosphere with wind. LBM results are compared with solutions of the equations of acoustics. It is found that the LBM works well for sound waves, but dissipation of sound waves with the LBM is generally much larger than real dissipation of sound waves in air. To circumvent this problem it is proposed here to use the LBM for assessing the excess sound level, i.e. the difference between the sound level and the free-field sound level. The effect of dissipation on the excess sound level is much smaller than the effect on the sound level, so the LBM can be used to estimate the excess sound level for a non-dissipative atmosphere, which is a useful quantity in atmospheric acoustics. To reduce dissipation in an LBM simulation two approaches are considered: i) reduction of the kinematic viscosity and ii) reduction of the lattice spacing.

Highlights

In the scientific field of computational fluid dynamics, various numerical methods have been developed for simulating fluid flow
It is concluded here that direct application of the lattice Boltzmann method (LBM) in acoustics is restricted to cases with small propagation distances and low sound frequencies
This article has presented a practical approach for simulating sound propagation in the atmosphere with the lattice Boltzmann method (LBM) for fluid flow

Summary

Introduction

In the scientific field of computational fluid dynamics, various numerical methods have been developed for simulating fluid flow. Conventional methods are based on the differential equations for mass and momentum conservation in a fluid, i.e. the continuity equation and the Navier Stokes equations [1,2]. An alternative method is the lattice Boltzmann method (LBM) for simulating fluid flow. The LBM has some advantages over conventional methods of computational fluid dynamics: i) application of the LBM to complex geometries is easy and ii) LBM algorithms are suitable for implementation on parallel platforms. The basis of the LBM is the Boltzmann equation from kinetic gas theory [1]. LBM solutions agree with solutions of the Navier Stokes and continuity equations [4]

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